Use the figure below to list the slopes m₁, m₂, m3, and m4 in order of decreasing size.

I'm confused, I'm not sure if the 12 you added to the problem is like the number of the problem or part of the problem, but my answer is going to be with the 12 as part of the problem.

Answer:  19/4 or 4 3/4 or 4.75

Step-by-step explanation: First you have to use the PEMDAS, which means first you have to do the parenthesis first, so add the 1/4 to the 1/3 which equals 7/12. so do that to the second power and then multiply the 12 and add the 2/3 which gets you 19/4

Answer:

What is a linear function? A linear function is a function whose graph is a straight line. The rate of change of a linear function is constant. The function shown in the graph below, y = x + 2, is an example of a linear function.

Graph of linear function

Graph of linear function

A linear function has a constant rate of change. The rate of change is the slope of the linear function. In the linear function shown above, the rate of change is 1. For every increase of one in the independent variable, x, there is a corresponding increase of one in the dependent variable, y. This gives a slope of 1/1 = 1.

A linear function is typically given in the form y = mx + b, where m is equal to the slope, or constant rate of change.

Examples of linear functions include:

If a person drives at a constant speed, the relationship between the time spent driving (independent variable) and the distance traveled (dependent variable) will remain constant.

Assuming no change in price, the relationship between the number of pounds of bananas a person buys (independent variable) and the total cost of the bananas (dependent variable) will remain constant.

If a person earns an hourly wage at their job, the relationship between the time spent working (independent variable) and the amount earned (dependent variable) will remain constant.

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Exponential Functions

What is an exponential function? An exponential function is a function that involves exponents and whose graph is a smooth curve. The rate of change in an exponential function is not constant. The functions shown in the graph below, y = 0.5x and y = 2x, are examples of exponential functions.

Graphs of exponential functions

Graphs of exponential functions

An exponential function does not have a constant rate of change. The rate of change in an exponential function is the value of the independent variable, x. As the value of x increases or decreases, the rate of change increases or decreases as well. Rather than a constant change, as in the linear function, there is a percent change.

An exponential function is typically given in the form y = (1 + r)x, where r represents the percent change.

Examples of exponential functions include:

Step-by-step explanation:

Answer:

Angle ABC is a right angle. So option C is correct.

What is the right triangle?

A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse.

The angle of a right angle is always 90 degrees.

IT is given that the Angle A B C is intersected by a line to form angles 25 degrees and 65 degrees.

If we add up 25 and 65 degrees, we get 90 degrees.

25 + 65 = 90

Thus, Angle ABC is a right angle because right angles are 90 degrees.

Therefore Angle ABC is a right angle. So option C is correct.

Step-by-step explanation:

he can paint ( 4 / 7 ) * 91 paintings in 4 weeks

4 / 7 = 0.57142857142

0.57142857142 * 91 = 52 paintings in 4 weeks

Answer:

the second one

Step-by-step explanation:

Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:

PV = A *\((1 - (1 + r)^(-n)) / r\)

Where:

PV = Present value

A = Annual payment or cash flow

r = Interest rate per period

n = Number of periods

In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).

Using the formula and substituting the given values, we can calculate the present value:

PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)

Calculating this expression:

PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)

= 13000 * (1 - 0.46318) / 0.10

= 13000 * 0.53682 / 0.10

= 6977.66 / 0.10

= 69776.6

Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

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The quadratic equation in standard form is:

ax^2 + bx + c = 25x^2 - 36x + 0

To factor this quadratic equation, we can first factor out the common factor of x:

25x^2 - 36x + 0 = x(25x - 36)

Now we can see that we have a quadratic expression inside the parentheses that can be factored further. To do so, we need to find two numbers whose product is 25 * (-36) = -900 and whose sum is -36. These numbers are -40 and 4:

25x^2 - 36x + 0 = x(25x - 36) = x(5x - 4)(5x - 32)

Therefore, the factored form of the quadratic equation is:

25x^2 - 36x + 0 = x(5x - 4)(5x - 32)

Rounding to 3 significant figures, average speed is 70.6 mph

Distance refers to the extent or length of space between two points. It is a scalar quantity that describes the separation between two points in a one-dimensional, two-dimensional, or three-dimensional space. Distance is usually measured in units such as meters, kilometers, miles, feet, or yards, depending on the system of measurement being used.

To calculate the lower bound for the average speed of the journey, we need to divide the distance travelled by the time taken, but we have to use the lower bound values of distance and time.

Lower bound distance = 235 - 2.5 (since the distance is given to the nearest 5 miles, we subtract half of 5 to get the lower bound value) = 232.5 miles

Lower bound time = 200 - 2.5 (since the time is given to the nearest 5 minutes, we subtract half of 5 to get the lower bound value) = 197.5 minutes

197.5 minutes ÷ 60 = 3.292 hours

Therefore, the lower bound for the average speed of the journey is:

Average speed = Lower bound distance ÷ Lower bound time = 232.5 miles ÷ 3.292 hours ≈ 70.648 mph

Rounding to 3 significant figures, we get the final answer:

Average speed = 70.6 mph

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Therefore, the average American eats 13.552 more grams of salt per week than the Centers for Disease Control and Prevention recommend.

Multiplication is a mathematical operation used to find the product of two or more numbers. The result of multiplication is called the product. It is represented by the symbol "×" or "*", and the numbers being multiplied are called factors. Multiplication is a way of adding multiple numbers of the same value. Similarly, multiplication can also be thought of as repeated addition of one number. Multiplication has many practical applications in everyday life, such as calculating the total cost of multiple items at a given price or determining the area of a rectangular surface by multiplying its length and width. It is also an essential part of higher-level mathematics, such as algebra and calculus.

Here,

There are 7 days in a week, so to find the total amount of salt the average American eats in a week, we need to multiply the daily amount by 7:

3.436 grams/day * 7 days = 24.052 grams/week

To find the recommended amount for a week, we simply multiply the daily recommendation by 7:

1.5 grams/day * 7 days = 10.5 grams/week

The difference between these two amounts is:

24.052 grams/week - 10.5 grams/week = 13.552 grams/week

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Start by finding the values on the linear portion of the piecewise function for 2 and -2

then, start graphing a straight horizontal line at y=-3 until x=-2

then, draw a line until (2,5)

finally, draw a straight line at y=3, and use an open circle since the value for x=2 is 5 and not 3

Answer:

Step-by-step explanation:

We would set up the hypothesis test.

For the null hypothesis,

p = 51/100 = 0.51

For the alternative hypothesis,

P ≠ 0.51

Considering the population proportion, probability of success, p = 0.51

q = probability of failure = 1 - p

q = 1 - 0.51 = 0.49

Considering the sample,

Sample proportion, P = x/n

Where

x = number of success = 278

n = number of samples = 800

P = 278/800 = 0.35

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

z = (0.35 - 0.51)/√(0.51 × 0.49)/800 = - 9.05

Recall, population proportion, P = 0.45

The difference between sample proportion and population proportion(p - P) is 0.51 - 0.35 = 0.16

Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.51 - 0.16 = 0.35

the p for the right tail is 0.51 + 0.16 = 0.67

These proportions are lower and higher than the null proportion. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area

From the normal distribution table, the area below the test z score in the left tail is < 0.00001

We would double this area to include the area in the right tail of z = 9.05 Thus

p < 0.00001 × 2

p < 0.00002

Since alpha, 0.01 > than the p value, then we would reject the null hypothesis.

Therefore, at 5% significance level, we can conclude that parents feel differently today than they did twenty years​ ago.

The true statement about the function is C. function f and function g are not inverse because f{g(x)} = g{f(x)} .

An inverse function or an anti function, which can reverse into another function.In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by 'f' or 'F', then the inverse function is denoted by f-1 or F-1.

now the given functions are,

f(x) = √(2x + 2) and

g(x) = (x^2 -2)/2

Now,

f{g(x)} = f{(x^2 -2)/2}

         = √(2(x^2 -2)/2 + 2)

         = √ x^2 -2 + 2

f{g(x)} = √ x^2

f{g(x)} =  x

Now,

g{f(x)} = g{ √(2x + 2)}

         = (√(2x + 2)^2 -2)/2

         = (2x + 2) -2 /2

         = 2x/2

f{g(x)} = x

Here we see that ,

f{g(x)} = g{f(x)}

Hence f and g are not inverses.

∴The true statement about the function is C. function f and function g are not inverse because f{g(x)} = g{f(x)} .

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To complete the sequence "7444> →→19-", we need to find the missing terms that fit the pattern established by the given numbers. Let's analyze the sequence and identify any discernible pattern or rule.

Looking at the sequence, we can observe that each number is decreasing by a certain value. In this case, the first number is 7444, and the second number is 19, indicating a decrease of 7425. Now, we need to continue this pattern.

To find the third missing term, we subtract 7425 from 19, resulting in -7406. Therefore, the third missing term is -7406

To find the fourth missing term, we subtract 7425 from -7406, resulting in -14831. Therefore, the fourth missing term is -14831.

To find the fifth missing term, we subtract 7425 from -14831, resulting in -22256. Therefore, the fifth missing term is -22256.

Therefore, the completed sequence is:

7444> →→19- → -7406 → -14831 → -22256

Each term in the sequence is obtained by subtracting 7425 from the previous term.

It's important to note that this solution assumes a linear pattern in which the same subtraction value is applied to each term. However, without additional context or information about the sequence, there could be alternative patterns or interpretations.

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The dimensions of the rectangular garden which minimize the cost is equal to 9.6ft and 14.6ft respectively.

As given in the question,

Cost of brick wall is equal to $40/ft

Cost of metal fencing is equal to $20/ft

Let 'x' and 'y' are the dimensions of the rectangular garden

Area of the rectangular garden = 142 square feet

⇒ 142 = xy

⇒x = 142/y

Costing of four side fencing 'C' = 40x + 20x + 20y + 20y

⇒ C = 60x + 40y

⇒C = 60(142/y) + 40y

⇒C = 8520/y + 40y

Differentiate with respect to y

dC/dy = -8520/ y² + 40

Put dC/dy = 0

-8520/ y² + 40 = 0

⇒y² = 8520/40

⇒y = √213

⇒ y= 14.6 ft

⇒ x= 142/14.6

     = 9.7 ft

Therefore, the dimensions of the rectangular garden with the given area which minimize the cost is equal to 14.6ft and 9.7ft.

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The median of the data set is 21, the upper and lower quartile is 27 and 13 respectively.

The median of a set of data is the middle value when the data is arranged in order from least to greatest or from greatest to least. If the data set has an odd number of values, the median is the middle value. If the data set has an even number of values, the median is the average of the two middle values.

To find the median, you first need to put the data in order from least to greatest or from greatest to least. Then, if the number of data points is odd, the median is the middle value. If the number of data points is even, you find the average of the two middle values.

From the data given;

10,11,13,18,19,21,22,25,27,30,32

The median is 21

The upper quartile is 27

The lower quartile is 13

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Answer:

Multiply each side by 6

Step-by-step explanation:

27 = m/6 - 3

Add 3 to each side

27+3 = m/6 - 3+3

30 = m/6

Multiply each side by 6

30*6 = m/6*6

180 = m

The value of the inverse function f-¹ (3) is (e) 11

From the question, we have the following parameters that can be used in our computation:

f(x) = x - 8

To calculate the inverse value at f-¹ (3)

We set the value to 3

using the above as a guide, we have the following:

x - 8 = 3

Evaluate the like terms

x = 11

Hence, the value of the inverse function is (e) 11

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Complete question

if f(x) = x - 8, what is the value of f-¹ (3)?

The expression 1 2/5 + 2 2/3 using fifteenths is 3 + 6/15 + 10/15

From the question, we have the following parameters that can be used in our computation:

1 2/5 + 2 2/3

3 + 2/5 + 2/3

To rewrite the expression using fifteenths, we multiply the numerator and the denominator of the fractions by the same number

In this case, we use 3 and 5

So, we have

3 + 2/5 * 3/3 + 2/3 * 5/5

Evaluate the products

3 + 6/15 + 10/15

Hence, the expression using fifteenths is 3 + 6/15 + 10/15

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Answer:30

Step-by-step explanation:

Answer:

0.253 m/s

Step-by-step explanation:

radius r of the circular rise = 13 mm = 0.013 m

apparent weight loss = 50%

acceleration of the new weight = 0.5 x 9.81 = 4.905 m/s^2

centripetal acceleration = 9.81 -  4.905 =  4.905 m/s^2

centripetal acceleration = \(\frac{v^{2} }{r}\)

where v is the acceleration at the rise and r is the radius of the rise

centripetal force = \(\frac{v^{2} }{r}\)  = \(\frac{v^{2} }{0.013}\)

4.905 = \(\frac{v^{2} }{0.013}\)

\(v^{2}\) = 0.063765

v = \(\sqrt{0.063765}\) = 0.253 m/s

The value of E(x) is 0.8695 and Var(x) is 0.5877

From the question, we have the following parameters that can be used in our computation:

n = 23

x = 4

k = 5

The value of E(x) is calculated as

E(x) = xk/N

Substitute the known values in the above equation, so, we have the following representation

E(x) = 4 * 5/23

E(x) = 0.8695

This is calculated as

Var(x) = E(x) * (1 - k/n) * ([n - x]/[n - 1])

Substitute the known values in the above equation, so, we have the following representation

Var(x) = (4 * 5/23) * (1 - 5/23) * ([23 - 4]/[23 - 1])

Evaluate

Var(x) = 0.5877

HEnce, the variance is 0.5877

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Answer:

Here's an interesting project idea for mathematics that can relate three different topics:

Topic 1: Fractals

Topic 2: Chaos Theory

Topic 3: Differential Equations

Research Question: Can fractals be used to model chaotic systems described by differential equations?

In this project, you can explore the concept of fractals and their applications in modeling complex systems. You can also delve into chaos theory and differential equations to understand how they are used to describe chaotic systems. By combining these three topics, you can investigate whether fractals can provide a better understanding of chaotic systems by modeling them more accurately.

Your research paper can cover the following areas:

Introduction: Provide an overview of fractals, chaos theory, and differential equations, and explain their relevance to the research question.

Fractals: Discuss the properties of fractals and how they can be used to model complex systems. Provide examples of fractals in nature and technology.

Chaos Theory: Explain the concept of chaos and how it is described by differential equations. Discuss the importance of chaos theory in understanding complex systems.

Differential Equations: Provide an overview of differential equations and their applications in physics, engineering, and other fields. Explain how differential equations are used to model chaotic systems.

Combining the three topics: Explain how fractals can be used to model chaotic systems described by differential equations. Provide examples of fractals used in modeling chaotic systems and compare the results to traditional methods.

Conclusion: Summarize the findings of your research and discuss the implications of using fractals to model chaotic systems.

Overall, this project can be a challenging and rewarding exploration of the interplay between three different mathematical topics.

Step-by-step explanation:

80 inches in standard notation using feet and inches would be expressed as 6 ft 8 inches by converting inches into feet and inches.

The solution to the given problem is to use some standard conversion units that are:

Solution:

As mentioned above that one inch is equal to 0.8333 foot therefore

1 foot = 12 inches

then,

80 inches would be equal to

= \(\frac{80}{12}\) ft

= \(\frac{20}{3}\) ft

= 6ft 8 inches

= 6' 8"

Thus, 80 inches in standard notation using feet and inches would be expressed as 6 ft 8 inches by converting inches into feet and inches.

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Answer: 39

Step-by-step explanation:

30-8=22

22/2=11

11+2=13

13 times 3 =39

Then, multiply this result by 100 to get the percentage. In this case, 120 is 80% of 150.

To use a double number line diagram to find what percent 120 is of 150, you need to create a diagram with two parallel lines. On the top line, mark 150 at one end and 100 at the other.

On the bottom line, mark 120 at one end and leave the other end blank. Then, draw diagonal lines connecting 120 on the bottom line to 150 on the top line and 100 on the top line to the blank end of the bottom line.

This creates two triangles. The height of the triangle with 120 is the percentage you're looking for.

To find this percentage, divide the length of the diagonal line connecting 120 and 150 by the length of the diagonal line connecting 100 and the blank end of the bottom line.

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Answer: D

Step-by-step explanation:

Answer:

100-mn

Step-by-step explanation:

Answer:

\(\Huge \boxed{\text{13.66$\%$}}\)

Step-by-step explanation:

To find the rate, we need to use the following formula:

\(\LARGE \boxed{ \boxed{\text{Rate = $\frac{\text{Portion}}{\text{Base}}$$\times$100}}}\)

Where "Portion" is the part of the whole and "Base" is the whole.

Now, let's plug in the given values:

\(\large \text{Rate = $\frac{\text{50}}{\text{366}}$$\times$100 = 13.66 (Rounded to the nearest tenth of a percent)}\)

Therefore, the rate is 13.66% (rounded to the nearest tenth of a percent).

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Answer:

34/45

Step-by-step explanation THERE IS NO NEED 5/9 +1/5=34/45

Answer:

$38.08

Step-by-step explanation:

12% of 34.00 as an equation would be \(34*0.12\), \(34*0.12=4.08\) so we add 4.08 to the total of the lunch already. \(34.00+4.08=38.08\). So the answer is $38.08. Hope this helps :)